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A NonHolonomic Control System

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Title: A NonHolonomic Control System


1
A Non-Holonomic Control System
  • Matthew Bott

2
The Aim
  • To produce a system capable of following a smooth
    path through a small number of variables.
  • This system should be capable of being used on
    any robotic system, particularly non-Holonomic
    situations.
  • This system should be able to adapt the smooth
    path, whilst, when possible, retaining smoothness
    in the event of unforeseeable circumstances.

3
An Example
A robot navigating non-holonomically from one
position and orientation to another along a
smooth path, when a global map of the environment
is unavailable. If obstacles should be
encountered, the system should be able to adapt
its configuration path to avoid the obstacles,
whilst still proceeding towards the goal.
4
Navigation
5
The General Method
  • A spline is calculated connecting the initial and
    end conditions
  • A nearby subgoal is set some way along this
    spline.
  • The subgoal is approximately attained via
    gradient descent of the control parameters
  • The spline then adapts to compensate for the
    actual configuration state realised.
  • Further subgoals are then set and attempted until
    the goal is attained.

6
Subgoal Chaining
Finish
Path
Subgoal
Start
7
Adaptation
Finish
Adapted Spline
Original Spline
Old Subgoal
New Subgoal
Start
Actual Path
8
The Initial Non-Holonomic Task
  • Rolling Disc
  • Control the movement of a rolling disc
  • Along a smooth path
  • From one x, y, and orientation, to another.
  • Control Parameters
  • Roll
  • Spin

9
The Rolling Disc
10
What are non-Holonomics?
  • Essentially controllable non-Holonomics are that,
    whilst all positions and orientations may be
    realisable, all paths are not.
  • For example, imagine a car, whilst it is possible
    for it to be in any position on the road, it is
    not possible for it to move sideways.

11
Non-Holonomics
  • Start and end parameters do not define the
    solution
  • Only certain configuration paths are possible
  • The configuration resulting from a given control
    variation may be known, but the control sequence
    resulting in a desired configuration state is
    not.
  • Finding a correct sequence of changes in control
    parameters dynamically, is essential for the
    solution
  • The correct actions, in the wrong sequence will
    not result in success
  • Recognised as difficult to solve!

12
Non-realisable Path Example
13
Attempts so far
  • Several issues attacked through continually
    refined strategies
  • No complete success so far, but enough to ensure
    publishable steady progress
  • System has been in development for 9 months

14
Euclidean Distance Method Principle
  • Intuitive
  • Distance from current state to the goal
  • Decreasing the distance decreases the error
  • System is drawn towards the goal

15
Euclidean Distance Problems
  • High Strain Paths
  • The ideal spline is not adhered to
  • Occasional phenomena
  • Reversing
  • Reverse Parking

16
High Strain Path
17
Strain Method Principle
  • The spline plots the minimal strain path
  • This is how smoothest path is defined
  • Therefore calculating the strain of the proposed
    path, and using strain in the gradient descent
    process, will encourage the smoothest path to be
    produced when the ideal spline is not realisable

18
Strain Method Problems
  • Bad error surface
  • Ravine effect at goal

19
Current Status
  • 2 Systems
  • A fixed spline can be followed, when realisable,
    with constant disc movement
  • A spline can be followed in an adaptable manner,
    when realisable, though with non-constant disc
    movement.

20
Current System 1
  • Euclidean Distance based
  • The spline is fixed, until proven necessary to
    adapt
  • Therefore the subgoals are fixed
  • Therefore low strain path is produced
  • Strength Constant Movement Possible
  • Weakness non-adapting spline

21
Current System 2
  • Euclidean Distance based
  • Spline adapts
  • Therefore low strain path is produced
  • Strength constantly adapting spline
  • Weakness Requires Stop and Think

22
Current Aim
  • To make the adaptable spline capable of constant
    disc movement
  • Either remove stop and think from 2
  • Or develop good trigger system for 1

23
The Future (6-12 months)
  • Finish the Rolling Disc problem
  • Obstacle avoidance
  • Differential drive
  • Tackle problems with unrealisable smooth paths,
    through techniques such as strain potential

24
The Future (Grand Plan)
  • Generic smooth motion demonstrated through robots
    capable of major types of challenging motion.
  • E.g.
  • Obstacle Navigation
  • Non-Holonomic Motion
  • Dynamic Stability
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